1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

1.2 Data: The COVID_19 Data-Set

The data to process is described in:

https://zenodo.org/record/4156647#.Y1bSF3bMKUk

IR Saliva Testing Dataset

10.5281/zenodo.4156647 https://doi.org/10.5281/zenodo.4156647

I added a column to the data identifying the repeated experiments.


SalivaIR <- as.data.frame(read_excel("~/GitHub/FCA/Data/SalivaThermal_Source_Data_2.xlsx"))


SalivaIR_set1 <- subset(SalivaIR,RepID==1)
rownames(SalivaIR_set1) <- SalivaIR_set1$ID
SalivaIR_set1$RepID <- NULL
SalivaIR_set1$ID <- NULL
SalivaIR_set1$Ct <- NULL

SalivaIR_set2 <- subset(SalivaIR,RepID==2)
rownames(SalivaIR_set2) <- SalivaIR_set2$ID
SalivaIR_set2$RepID <- NULL
SalivaIR_set2$ID <- NULL
SalivaIR_set2$Ct <- NULL

SalivaIR_set3 <- subset(SalivaIR,RepID==3)
rownames(SalivaIR_set3) <- SalivaIR_set3$ID
SalivaIR_set3$RepID <- NULL
SalivaIR_set3$ID <- NULL
SalivaIR_set3$Ct <- NULL

SalivaIR_Avg <- (SalivaIR_set1 + SalivaIR_set2 + SalivaIR_set3)/3


colnames(SalivaIR_Avg) <- paste("V",colnames(SalivaIR_Avg),sep="_")

SalivaIR_Avg$class <- 1*(str_detect(rownames(SalivaIR_Avg),"P"))

pander::pander(table(SalivaIR_Avg$class))
0 1
30 31

1.2.0.1 Standarize the names for the reporting

studyName <- "IRSaliva"
dataframe <- SalivaIR_Avg
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))
rows col
61 251
pander::pander(table(dataframe[,outcome]))
0 1
30 31

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns


  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.999994

1.5 The decorrelation


DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 224 , Uni p: 0.04988877 , Uncorrelated Base: 1 , Outcome-Driven Size: 0 , Base Size: 1 
#> 
#> 
 1 <R=1.000,thr=0.900,N=  224>, Top: 1( 223 )[ 1 : 1 Fa= 1 : 0.900 ]( 1 , 223 , 0 ),<|>Tot Used: 224 , Added: 223 , Zero Std: 0 , Max Cor: 1.000
#> 
 2 <R=1.000,thr=0.900,N=  224>, Top: 3( 93 )[ 1 : 3 Fa= 4 : 0.900 ]( 3 , 154 , 1 ),<|>Tot Used: 224 , Added: 154 , Zero Std: 0 , Max Cor: 1.000
#> 
 3 <R=1.000,thr=0.900,N=  224>, Top: 10( 24 )=( 1 )[ 2 : 10 Fa= 14 : 0.935 ]( 10 , 131 , 4 ),<|>Tot Used: 224 , Added: 131 , Zero Std: 0 , Max Cor: 1.000
#> 
 4 <R=1.000,thr=0.900,N=  224>, Top: 18( 3 )[ 1 : 18 Fa= 32 : 0.900 ]( 18 , 147 , 14 ),<|>Tot Used: 224 , Added: 147 , Zero Std: 0 , Max Cor: 1.000
#> 
 5 <R=1.000,thr=0.900,N=  224>, Top: 35( 5 )[ 1 : 35 Fa= 67 : 0.900 ]( 35 , 134 , 32 ),<|>Tot Used: 224 , Added: 134 , Zero Std: 0 , Max Cor: 0.999
#> 
 6 <R=0.999,thr=0.900,N=  224>, Top: 34( 8 )[ 1 : 34 Fa= 101 : 0.900 ]( 34 , 96 , 67 ),<|>Tot Used: 224 , Added: 96 , Zero Std: 0 , Max Cor: 0.998
#> 
 7 <R=0.998,thr=0.900,N=  224>, Top: 25( 2 )[ 1 : 25 Fa= 126 : 0.900 ]( 25 , 47 , 101 ),<|>Tot Used: 224 , Added: 47 , Zero Std: 0 , Max Cor: 0.996
#> 
 8 <R=0.996,thr=0.900,N=  224>, Top: 11( 3 )[ 1 : 11 Fa= 137 : 0.900 ]( 11 , 15 , 126 ),<|>Tot Used: 224 , Added: 15 , Zero Std: 0 , Max Cor: 0.934
#> 
 9 <R=0.934,thr=0.900,N=  224>, Top: 2( 1 )[ 1 : 2 Fa= 139 : 0.900 ]( 2 , 2 , 137 ),<|>Tot Used: 224 , Added: 2 , Zero Std: 0 , Max Cor: 0.897
#> 
 10 <R=0.897,thr=0.800,N=   76>, Top: 33( 1 )[ 1 : 33 Fa= 145 : 0.800 ]( 29 , 39 , 139 ),<|>Tot Used: 224 , Added: 39 , Zero Std: 0 , Max Cor: 0.994
#> 
 11 <R=0.994,thr=0.900,N=   30>, Top: 15( 1 )[ 1 : 15 Fa= 151 : 0.900 ]( 15 , 15 , 145 ),<|>Tot Used: 224 , Added: 15 , Zero Std: 0 , Max Cor: 0.970
#> 
 12 <R=0.970,thr=0.900,N=   30>, Top: 5( 1 )[ 1 : 5 Fa= 153 : 0.900 ]( 5 , 5 , 151 ),<|>Tot Used: 224 , Added: 5 , Zero Std: 0 , Max Cor: 0.993
#> 
 13 <R=0.993,thr=0.900,N=   30>, Top: 3( 1 )[ 1 : 3 Fa= 153 : 0.900 ]( 3 , 3 , 153 ),<|>Tot Used: 224 , Added: 3 , Zero Std: 0 , Max Cor: 0.940
#> 
 14 <R=0.940,thr=0.900,N=   30>, Top: 1( 1 )[ 1 : 1 Fa= 153 : 0.900 ]( 1 , 1 , 153 ),<|>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.883
#> 
 15 <R=0.883,thr=0.800,N=   21>, Top: 9( 2 )[ 1 : 9 Fa= 154 : 0.800 ]( 9 , 11 , 153 ),<|>Tot Used: 224 , Added: 11 , Zero Std: 0 , Max Cor: 0.960
#> 
 16 <R=0.960,thr=0.900,N=    4>, Top: 2( 1 )[ 1 : 2 Fa= 154 : 0.900 ]( 2 , 2 , 154 ),<|>Tot Used: 224 , Added: 2 , Zero Std: 0 , Max Cor: 0.979
#> 
 17 <R=0.979,thr=0.900,N=    4>, Top: 2( 1 )[ 1 : 2 Fa= 154 : 0.900 ]( 2 , 2 , 154 ),<|>Tot Used: 224 , Added: 2 , Zero Std: 0 , Max Cor: 0.927
#> 
 18 <R=0.927,thr=0.900,N=    4>, Top: 1( 1 )[ 1 : 1 Fa= 154 : 0.900 ]( 1 , 1 , 154 ),<|>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.848
#> 
 19 <R=0.848,thr=0.800,N=    2>, Top: 1( 1 )[ 1 : 1 Fa= 154 : 0.800 ]( 1 , 1 , 154 ),<|>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.799
#> 
 20 <R=0.799,thr=0.800,N=    2>
#> 
 [ 20 ], 0.7985213 Decor Dimension: 224 Nused: 224 . Cor to Base: 223 , ABase: 1 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

5.5

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

0.0328

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

5.08

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

0.843

1.5.1 The decorrelation matrix


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPSTM <- attr(DEdataframe,"UPSTM")
  
  gplots::heatmap.2(1.0*(abs(UPSTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.7985213

1.8 U-MAP Visualization of features

1.8.1 The UMAP based on LASSO on Raw Data


if (nrow(dataframe) < 1000)
{
  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}

1.8.2 The decorralted UMAP

if (nrow(dataframe) < 1000)
{

  datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}

1.9 Univariate Analysis

1.9.1 Univariate



univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : V_1064 200 : V_854




univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_V_1064 200 : La_V_854

1.9.2 Final Table


univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
V_908 0.221 0.128 0.261 0.117 0.579 0.596
V_906 0.220 0.127 0.261 0.117 0.585 0.596
V_904 0.220 0.127 0.261 0.117 0.592 0.596
V_892 0.219 0.127 0.261 0.121 0.626 0.596
V_890 0.219 0.127 0.261 0.121 0.616 0.596
V_888 0.219 0.127 0.261 0.122 0.603 0.596
V_912 0.223 0.129 0.263 0.117 0.604 0.595
V_910 0.222 0.128 0.262 0.117 0.587 0.595
V_896 0.220 0.127 0.261 0.120 0.620 0.595
V_894 0.219 0.127 0.261 0.121 0.625 0.595


topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
La_V_1048 3.02e-04 4.30e-03 -3.99e-03 3.15e-03 0.8394 0.841
La_V_1226 1.27e-03 1.55e-03 2.82e-03 1.49e-03 0.8181 0.803
La_V_902 -2.20e-06 1.72e-05 -2.01e-05 2.28e-05 0.6481 0.772
La_V_1110 4.48e-03 1.90e-02 1.95e-02 1.21e-02 0.1718 0.765
La_V_1196 5.71e-05 2.44e-04 2.81e-04 3.86e-04 0.2432 0.749
La_V_1034 2.35e-04 1.19e-03 -6.05e-04 5.33e-04 0.9599 0.742
La_V_848 2.51e-04 2.17e-03 -6.34e-04 9.82e-04 0.1939 0.734
La_V_1032 3.10e-03 9.45e-03 9.68e-03 7.58e-03 0.9605 0.733
La_V_892 -5.57e-06 4.67e-06 -1.94e-06 5.19e-06 0.9945 0.732
La_V_1252 -5.51e-03 8.34e-03 -1.32e-02 1.29e-02 0.0145 0.726

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))
mean total fraction
5.75 223 0.996

theCharformulas <- attr(dc,"LatentCharFormulas")


finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])
  DecorFormula caseMean caseStd controlMean controlStd controlKSP ROCAUC RAWAUC fscores
La_V_1048 - (9.70e-03)V_1300 - (0.413)V_1064 + V_1048 - (0.599)V_1032 3.02e-04 4.30e-03 -3.99e-03 3.15e-03 0.8394 0.841 0.545 2
La_V_1226 + (0.046)V_1300 - (1.034)V_1228 + V_1226 1.27e-03 1.55e-03 2.82e-03 1.49e-03 0.8181 0.803 0.546 1
La_V_902 - (1.21e-04)V_1300 + (0.417)V_906 - (1.213)V_904 + V_902 - (0.471)V_896 + (0.271)V_894 - (3.14e-03)V_868 -2.20e-06 1.72e-05 -2.01e-05 2.28e-05 0.6481 0.772 0.594 -6
La_V_1110 - (0.123)V_1300 + V_1110 - (0.840)V_1064 4.48e-03 1.90e-02 1.95e-02 1.21e-02 0.1718 0.765 0.561 14
La_V_1196 + (6.26e-03)V_1300 - (0.191)V_1206 + V_1196 - (0.813)V_1194 5.71e-05 2.44e-04 2.81e-04 3.86e-04 0.2432 0.749 0.567 5
La_V_1034 + (8.11e-03)V_1300 - (0.034)V_1064 + V_1034 - (0.979)V_1032 2.35e-04 1.19e-03 -6.05e-04 5.33e-04 0.9599 0.742 0.546 6
La_V_848 - (0.011)V_1300 + (1.038)V_868 - (2.013)V_860 + V_848 2.51e-04 2.17e-03 -6.34e-04 9.82e-04 0.1939 0.734 0.589 -3
La_V_1032 + (0.017)V_1300 + (1.769)V_1064 - (2.723)V_1056 + V_1032 3.10e-03 9.45e-03 9.68e-03 7.58e-03 0.9605 0.733 0.548 13
La_V_892 - (3.94e-05)V_1300 + (0.152)V_896 - (0.620)V_894 + V_892 - (0.762)V_890 + (0.231)V_888 - (1.47e-03)V_868 -5.57e-06 4.67e-06 -1.94e-06 5.19e-06 0.9945 0.732 0.596 -5
La_V_1252 - (1.045)V_1300 + V_1252 -5.51e-03 8.34e-03 -1.32e-02 1.29e-02 0.0145 0.726 0.538 13
V_908 NA 2.21e-01 1.28e-01 2.61e-01 1.17e-01 0.5785 0.596 0.596 NA
V_906 NA 2.20e-01 1.27e-01 2.61e-01 1.17e-01 0.5848 0.596 0.596 NA
V_904 NA 2.20e-01 1.27e-01 2.61e-01 1.17e-01 0.5918 0.596 0.596 NA
V_892 NA 2.19e-01 1.27e-01 2.61e-01 1.21e-01 0.6256 0.596 0.596 NA
V_890 NA 2.19e-01 1.27e-01 2.61e-01 1.21e-01 0.6163 0.596 0.596 NA
V_888 NA 2.19e-01 1.27e-01 2.61e-01 1.22e-01 0.6032 0.596 0.596 NA
V_912 NA 2.23e-01 1.29e-01 2.63e-01 1.17e-01 0.6041 0.595 0.595 NA
V_910 NA 2.22e-01 1.28e-01 2.62e-01 1.17e-01 0.5866 0.595 0.595 NA
V_896 NA 2.20e-01 1.27e-01 2.61e-01 1.20e-01 0.6202 0.595 0.595 NA
V_894 NA 2.19e-01 1.27e-01 2.61e-01 1.21e-01 0.6248 0.595 0.595 NA

1.10 Comparing IDeA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA


EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }


pander::pander(table(dataframe[,outcome],pr))
  0 1
0 30 0
1 17 14
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.721 0.592 0.829
3 se 0.452 0.273 0.640
4 sp 1.000 0.884 1.000
6 diag.or Inf NA Inf

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))
  0 1
0 26 4
1 1 30
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.918 0.819 0.973
3 se 0.968 0.833 0.999
4 sp 0.867 0.693 0.962
6 diag.or 195.000 20.484 1856.331

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))
  0 1
0 23 7
1 3 28
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.836 0.719 0.918
3 se 0.903 0.742 0.980
4 sp 0.767 0.577 0.901
6 diag.or 30.667 7.117 132.134


par(op)

1.11.1 EFA


  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }


  pander::pander(table(EFAdataframe[,outcome],pr))
  0 1
0 29 1
1 16 15
  pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.721 0.592 0.829
3 se 0.484 0.302 0.669
4 sp 0.967 0.828 0.999
6 diag.or 27.188 3.282 225.207
  par(op)